Proceedings of the Japan Academy, Series A, Mathematical Sciences

The number of semidihedral or modular extensions of a local field

Makoto Ito and Masakazu Yamagishi

Full-text: Open access


We calculate the number of Galois extensions, up to isomorphism, of a local field whose Galois groups are isomorphic to the semidihedral (resp. modular) group of order $2^m$ ($m\ge 4$).

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 83, Number 2 (2007), 10-13.

First available in Project Euclid: 5 March 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11S20: Galois theory

Local field $2$-extension


Ito, Makoto; Yamagishi, Masakazu. The number of semidihedral or modular extensions of a local field. Proc. Japan Acad. Ser. A Math. Sci. 83 (2007), no. 2, 10--13. doi:10.3792/pjaa.83.10.

Export citation


  • G. Fardoux, Sur les extensions pseudodiédrales d'un corps local, C. R. Acad. Sci. Paris Sér. A-B 277 (1973), A145– A148.
  • M. Ito, On $2$-extensions of a local field, Master's thesis, Nagoya Institute of Technology, 2007. (in Japanese).
  • C. U. Jensen, Finite groups as Galois groups over arbitrary fields, in Proceedings of the International Conference on Algebra, Part 2 (Novosibirsk, 1989), 435–448, Contemp. Math., Part 2, Amer. Math. Soc., Providence, RI, 1992.
  • M. Yamagishi, On the number of Galois $p$-extensions of a local field, Proc. Amer. Math. Soc. 123 (1995), no. 8, 2373–2380.